Final answer:
The equations y = 1/6x - 5 and y = 6x - 3 have slopes of 1/6 and 6 respectively. Since they are neither equal, implying not parallel, nor negative reciprocals of each other, implying not perpendicular, the lines are neither parallel nor perpendicular.
Step-by-step explanation:
To determine whether the equations are parallel, perpendicular, or neither, we must convert each equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. The first equation is already in slope-intercept form: y = 1/6x - 5, with a slope of 1/6.
The second equation can be rewritten as y = 6x - 3, which yields a slope of 6. Therefore, we have slopes of 1/6 and 6. In general, two lines are perpendicular if the product of their slopes is -1.
When we multiply 1/6 by 6, we get 1, not -1, thus these lines are not perpendicular. Since the slopes are not equal, the lines are not parallel either. The answer is c. Neither.